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THE PARAMETERIZED INTEGRAL INEQUALITIES INVOLVING TWICE-DIFFERENTIABLE GENERALIZED n-POLYNOMIAL CONVEXITY UNDER THE FRAMEWORK OF FRACTAL DOMAINS AND ITS APPLICATIONS

Author

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  • TINGSONG DU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang, Hubei 443002, P. R. China)

  • LEI XU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P. R. China)

  • XIAOMAN YUAN

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P. R. China)

Abstract

A fractal integral identity with the parameter Ï„ related to twice-differentiable mappings is first proposed in this paper. Based on the identity, the parameterized inequalities over the fractal domains are then derived for the mappings whose second-order derivatives in absolute value at certain powers are generalized n-polynomial convex, which is the main purpose of this investigation. Moreover, a series of fractal findings of some applications, involving the special mean values, the midpoint formulas, the moments of random variable and the wave equations on Cantor sets, are acquired correspondingly.

Suggested Citation

  • Tingsong Du & Lei Xu & Xiaoman Yuan, 2023. "THE PARAMETERIZED INTEGRAL INEQUALITIES INVOLVING TWICE-DIFFERENTIABLE GENERALIZED n-POLYNOMIAL CONVEXITY UNDER THE FRAMEWORK OF FRACTAL DOMAINS AND ITS APPLICATIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-25.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x2350069x
    DOI: 10.1142/S0218348X2350069X
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